Transcript CHAPTER 10

CHAPTER 10
Determining
How Costs Behave
Cost Functions
 A cost function is a mathematical
representation of how a cost changes with
changes in the level of an activity relating to
that cost
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-2
Cost Terminology
 Variable Costs – costs that change in total in
relation to some chosen activity or output
 Fixed Costs – costs that do not change in
total in relation to some chosen activity or
output
 Mixed Costs – costs that have both fixed and
variable components; also called
semivariable costs
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-3
Cost Function Assumptions
Variations in the level of a single activity (the
cost driver) explain the variations in the
related total costs
2. Cost behavior is approximated by a linear
cost function within the relevant range
1.

Graphically, the total cost versus the level of
a single activity related to that cost is a
straight line within the relevant rage
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-4
Bridging Accounting and Statistical
Terminology
Accounting
Statistics
Variable Cost
Slope
Fixed Cost
Intercept
Mixed Cost
Linear Cost Function
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-5
The Linear Cost Function
y = a + bX
The Independent
Variable:
The cost driver
The Dependent
Variable:
The cost that is
being predicted
The Intercept:
Fixed costs
The Slope of
the Line:
Variable cost
per unit
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-6
Fixed Cost Function, Graphically
Total Cost Function: Y = $10,000
$60,000
$50,000
$40,000
$30,000
$20,000
$10,000
$0
2000
4000
6000
8000
10000
12000
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-7
Variable Cost Function, Graphically
Total Cost Function: Y = $5X
$60,000
$50,000
$40,000
$30,000
$20,000
$10,000
$0
2000
4000
6000
8000
10000
12000
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-8
Total Cost Function, Graphically
Total Cost Function: Y = $10,000 + $5X
$70,000
$60,000
$50,000
$40,000
$30,000
$20,000
$10,000
$0
2000
4000
6000
8000
10000
12000
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-9
Cost Functions Combined
$70,000
$60,000
$50,000
$40,000
Variable Cost Y = $5X
Fixed Cost Y = $10,000
Total Cost Y = $10,000 + $5X
$30,000
$20,000
$10,000
$0
2000
4000
6000
8000
10000
12000
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-10
Criteria for Classifying Variable and
Fixed Components of a Cost
Choice of Cost Object – different objects
may result in different classification of the
same cost
2. Time Horizon – the longer the period, the
more likely the cost will be variable
3. Relevant Range – behavior is predictable
only within this band of activity
1.
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-11
Cause and Effect as It Relates to
Cost Drivers
 The most important issue in estimating a cost
function is determining whether a cause-andeffect relationship exists between the level of
an activity and the costs related to that level
of activity.
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-12
Cause and Effect as It Relates to
Cost Drivers
 A cause-and-effect relationship might arise as
a result of:



A physical relationship between the level of
activity and costs
A contractual agreement
Knowledge of operations
 Note: a high correlation (connection) between
activities and costs does not necessarily
mean causality
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-13
Cost Estimation Methods
Industrial Engineering Method
2. Conference Method
3. Account Analysis Method
4. Quantitative Analysis Methods
1.
1.
2.
High-Low Method
Regression Analysis
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-14
Industrial Engineering Method
 Estimates cost functions by analyzing the
relationship between inputs and outputs in
physical terms
 Includes time-and-motion studies
 Very thorough and detailed, but also costly
and time consuming
 Also called the Work-Measurement Method
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-15
Conference Method
 Estimates cost functions on the basis of
analysis and opinions about costs and their
drivers gathered from various departments of
a company
 Pools expert knowledge
 Reliance on opinions still makes this method
subjective
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-16
Account Analysis Method
 Estimates cost functions by classifying
various cost accounts as variable, fixed, or
mixed with respect to the identified level of
activity
 Is reasonably accurate, cost-effective, and
easy to use, but is subjective
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-17
Qualitative Analysis
 Uses a formal mathematical method to fit cost
functions to past data observations
 Advantage: results are objective
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-18
Steps in Estimating a Cost Function
Using Quantitative Analysis
1.
2.
3.
4.
5.
6.
Choose the dependent variable (the cost to be
predicted)
Identify the independent variable or cost driver
Collect data on the dependent variable and the cost
driver
Plot the data
Estimate the cost function using the High-Low
Method or Regression Analysis
Evaluate the cost driver of the estimated cost
function
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-19
High-Low Method
 Simplest method of quantitative analysis
 Uses only the highest and lowest observed
values
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-20
Steps in the High-Low Method
1.
Calculate variable cost per unit of activity
Variable
Cost per
Unit of Activity
=
{
Cost associated with
highest activity level
Highest activity level
-
Cost associated with
highest activity level
}
Lowest activity level
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-21
Steps in the High-Low Method
2.
Calculate Total Fixed Costs
Total Cost from either the highest or lowest activity level
– (Variable Cost per unit of activity X Activity associated with above total cost)
Fixed Costs
3.
Summarize by writing a linear equation
Y = Fixed costs + ( Variable cost per unit of Activity * Activity )
Y = FC + (VCu * X)
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-22
Regression Analysis
 Regression analysis is a statistical method that
measures the average amount of change in the
dependent variable associated with a unit change in
one or more independent variables
 Is more accurate than the High-Low method because
the regression equation estimates costs using
information from all observations; the High-Low
method uses only two observations
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-23
Types of Regression
 Simple – estimates the relationship between
the dependent variable and one independent
variable
 Multiple – estimates the relationship between
the dependent variable and two or more
independent variables
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-24
Terminology
 Goodness of Fit – indicates the strength of
the relationship between the cost driver and
costs
 Residual Term – measures the distance
between actual cost and estimated cost for
each observation
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-25
Criteria for Evaluating
Alternative Cost Drivers
Economic Plausibility
2. Goodness of Fit
3. Significance of the Independent Variable
1.
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-26
Nonlinear Cost Functions
1.
2.
3.
4.
5.
Economies of Scale
Quantity Discounts
Step Cost Functions – resources increase in “lotsizes,” not individual units
Learning Curves – labor hours consumed decrease
as workers learn their jobs and become better at
them
Experience Curve – broader application of learning
curve that includes downstream activities including
marketing and distribution
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-27
Types of Learning Curves
 Cumulative Average-Time Learning Model –
cumulative average time per unit declines by a
constant percentage each time the cumulative
quantity of units produced doubles
 Incremental Unit-Time Learning Model – incremental
time needed to produce the last unit declines by a
constant percentage each time the cumulative
quantity of units produced doubles
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-28
The Ideal Database
The database should contain numerous
reliably measured observations of the cost
driver and the costs
2. In relation to the cost driver, the database
should consider many values spanning a
wide range
1.
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-29
Data Problems
 The time period for measuring the dependent
variable does not match the period for
measuring the cost driver
 Fixed costs are allocated as if they are
variable
 Data are either not available for all
observations or are not uniformly reliable
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-30
Data Problems
 Extreme values of observations occur from
errors in recording costs
 There is no homogeneous relationship
between the cost driver and the individual
cost items in the dependent variable-cost
pool. A homogeneous relationship exists
when each activity whose costs are included
in the dependent variable has the same cost
driver
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-31
Data Problems
 The relationship between the cost driver and
the cost is not stationary
 Inflation has affected costs, the driver, or both
To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.
10-32